A fair die is thrown 5 times. What is the probability of getting point 1 on exactly 4 of the 5 throws?

Question

A fair die is thrown 5 times. What is the probability of getting point 1 on exactly 4 of the 5 throws?

Answer 1

Since the throws are independent, we multiply the probabilities of getting or not getting a 1 for each of the 5 tosses.

 

 

P(1) = 1/6 for getting 1.

 

P(not 1) = 5/6 for not getting 1.

 

 

P(1 in 4 out of 5 tosses) = (1/6)⁴(5/6) = 5/6⁵ = 5/7776 ≅ 1/1550